Klein Bottle

Klein-bottle-printJust a really short post to share our general excitement over having just about completed all of the objects from Multivariable Calculus. We just have a few more to print out. We will spend our remaining week(!) printing out some interesting topological objects – many of these directly from Thingiverse.

We printed one such object today. This is the Voronoi Klein Bottle from MadOverlord on Thingiverse. We printed this on the MakerBot 2X with a raft but no supports. After a moment’s thought one can see that the print succeeds (despite the short horizontal lines on the design) because the Voronoi cells are small enough. Interesting! The black filament also hides a few rough spots on the print.

The Klein bottle is named after Felix Klein (25 April 1849 – 22 June 1925), a German mathematician who saw many connections between Group Theory and Geometry. It is a one-sided surface and is a generalization of a Mobius strip. (In fact, it is topologically equivalent to two Mobius strips glued together along their boundaries.)

There are many fabulous descriptions of this topological object, one of my favorites is The Adventures of the Klein Bottle found on YouTube (from the wonderful folks at the Frei Universitat in Berlin).